Andrew is making cookies for his siblings. The recipe calls for 4.8 end style cups of sugar and 2 1/5 cups of flour. If he has already added 1/4 cup of flour, how much more flour does he need

Answer:

(x - 3) * 6 = 72

jack earns $ 15 an hour and samuel $12 an hour

Step-by-step explanation:

we know that samuel earns 3 dollars less than jack, let's say that "x" is what jack earns, in addition to this we know that samuel earns a total of 72 dollars in 6 hours, therefore we have to:

(x - 3) * 6 = 72

this would be the equation to determine x, we solve it:

6 * x - 18 = 72

6 * x = 72 + 18

x = 90/6

x = 15

which means that jack earns $ 15 an hour and samuel $12 an hour

Answer:

\(g(x) = \sqrt{\frac{1}{4}x +4}\)

Step-by-step explanation:

Given

\(f(x) = \sqrt{x + 2\)

Transformations:

1. Horizontal shrink by 1/4

2. Translation 2 units right

Required

Determine the new function

1. Horizontal shrink by 1/4

This implies that:

For:

\(f(x) = \sqrt{x + 2\)

After shrinking, the function is:

\(f'(\frac{1}{4}x) = \sqrt{\frac{1}{4}x + 2}\)

2. Translation 2 units right

For:

\(f'(\frac{1}{4}x) = \sqrt{\frac{1}{4}x + 2}\)

The right translation is given by:

\(g(x) = f(x + b)\)

Where b is the number of units translated.

So:

\(g(x) = f"(\frac{1}{4}x+2) = \sqrt{\frac{1}{4}x +2+ 2}\)

\(g(x) = f"(\frac{1}{4}x+2) = \sqrt{\frac{1}{4}x +4}\)

Hence:

\(g(x) = \sqrt{\frac{1}{4}x +4}\)

Parallel lines are lines that have equal slope

It is true that the two lines are parallel

The equations of the two lines are given as:

y = 5x + 1 and 2y - 10x + 3 = 0

Both equations are linear equations, and a linear equation is represented as:

y = mx + b

Where m represents the slope.

For equation L1, the slope is:

m = 5

For equation L2, we have:

\(2y - 10x + 3 = 0\)

Divide through by 2

\(y - 5x + 1.5 = 0\)

Make y the subject

\(y = 5x - 1.5\)

This means that the slope of equation L2 is also 5

When the slopes are equal, then the lines are parallel

Hence, the two lines are parallel

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Answer:

$20-$14=$6

Step-by-step explanation:

this is correct because if you give the $20 to them and the toy costs $14 then you subtract that from the amount you gave them then whatever is left is how much you get back.

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In the given proof, the phrase " There exists k = n+1 " is not a general practice to write.

option (d) is correct [ans]

An integer is a whole number that can be positive, negative, or zero, and does not include any fractional or decimal parts.

Integers are part of the set of numbers called the integers, which includes all positive numbers, negative numbers, and zero.

We write " Let k = n+1 or assume n = k+1".

And then, we say that, it is obvious that

n < k = n+1 < n+2 for any integer n.

Hence, option (d) is correct [ans]

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Answer:

look it upo

Step-by-step explanation:

Answer:

Hi! sorry bout the other guy he did the same thing to me ive been reporting all his answers and im sorry because it sucks anyways i hink its 80

Step-by-step explanation:

Answer:

Slope m = -3

y-intercept (0, 0)

General Formulas and Concepts:

Algebra I

Slope-Intercept Form: y = mx + b

Step-by-step explanation:

Step 1: Define

y = -3x

Step 2: Break Function

Identify Parts.

Slope m = -3

y-intercept b = 0

When 'a' is 10, 'c' is approximately 142.97. You can repeat this process for different values of 'a' to find corresponding values of 'c'. Keep in mind that there are infinitely many solutions to this equation

To use the elimination method to solve the equation 2a + c = 162.97, we need another equation with the same variables. However, as there is only one equation given, we cannot apply the elimination method directly.

The elimination method typically involves adding or subtracting equations to eliminate one of the variables, resulting in a new equation with only one variable. Since we have only one equation, we don't have the opportunity to eliminate variables using another equation.

In this case, we can solve the given equation directly by isolating one variable in terms of the other. Let's solve for 'c':

2a + c = 162.97

Rearrange the equation to isolate 'c':

c = 162.97 - 2a

Now, we have an expression for 'c' in terms of 'a'. This equation represents a line in the 'a-c' coordinate plane. We can choose any value for 'a', substitute it into the equation, and calculate the corresponding 'c' value.

For example, let's say we choose 'a' = 10:

c = 162.97 - 2(10)

c = 162.97 - 20

c = 142.97

So, when 'a' is 10, 'c' is approximately 142.97.

You can repeat this process for different values of 'a' to find corresponding values of 'c'. Keep in mind that there are infinitely many solutions to this equation since we have one equation and two variables.

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Answer:

yellow : 8

Red : 4

Step-by-step explanation:

Yellow : Y and Red : R

R : Y = 12

They need to add up to 12 because its the total.

We know that yellow is twice the amount so

4×2= 8

so if yellow was to be times by 2 itd be 8 which will still add up to 12.

The number of yellow fish should be 8 and the number of redfish be 4.

Since Jacob has 12 fish, all of them are either yellow or red. There are twice as much yellow fish as red fish.

Here we assume the redfish be x

So, the yellow be 2x

So

2x + x = 12

3x = 12

x = 4

So, redfish should be 4

And, the yellow fish should be 8

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The steps to be taken to determine the volume of the rectangular prism are:

Use A = bh to find the area of the base.

Use V = Bh to find the volume of the prism.

Volume of the prism, V = (228)(6) = 1,368 feet cubed.

A rectangular prism has a height, base, and width. The volume of the rectangular prism can be found by using the following steps:

Parameters are:

Length of prism = 9 and one-half feet,

Width of prism = 24 feet,

Height of prism = 6 feet

Given the dimensions of the rectangular prism above, do the following:

Find the area of the base of the rectangular prism:

Area of base = (9 1/2)(24) = 228 cm²

Find the Volume of the prism using V = Bh :

Volume of the prism = (228)(6) = 1,368 feet cubed.

Therefore, the steps to be taken to determine the volume of the rectangular prism are:

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Answer:

Therefore, the correct statements are A, B, and E.

Explanation:

Based on my knowledge, a vector is a quantity that has both magnitude and direction. A scalar is a quantity that has only magnitude. When a vector is multiplied by a scalar, the magnitude of the vector is multiplied by the absolute value of the scalar, and the direction of the vector is either preserved or reversed depending on the sign of the scalar.

To answer your question, we need to find the component form, magnitude, and direction of the scalar product –4⇀

.

- The component form of −4⇀

is obtained by multiplying each component of ⇀

by –4. Therefore, −4⇀

= ⟨–8, –12⟩. This means that statement A is true.

- The magnitude of −4⇀

is obtained by multiplying the magnitude of ⇀

by 4. The magnitude of ⇀

is √(2^2 + 3^2) = √13. Therefore, the magnitude of −4⇀

is 4√13. This means that statement B is true.

- The direction of −4⇀

is opposite to the direction of ⇀

because the scalar –4 is negative. This means that statement C is false.

- The vector −4⇀

is in the third quadrant because its components are both negative. This means that statement D is false.

- The direction of −4⇀

is 180° greater than the inverse tangent of its components because it is opposite to ⇀

. The inverse tangent of its components is tan^(-1)(–12/–8) = tan^(-1)(3/2). Therefore, the direction of −4⇀

is 180° + tan^(-1)(3/2). This means that statement E is true.

Therefore, the correct statements are A, B, and E.

Answer:

t ≤ 225r

Step-by-step explanation:

Distance = 225 miles

Time taken = t

Average speed = r miles per hour

Recall :

Speed = distance / time

Time, = distance / speed

t = 225 miles / r

All possible values of t :

t ≤ 225r

Answer:

9

Step-by-step explanation:

Eight times five is 40

40x225 is 9000

9000 divided by 1000=9

Answer: 9 liters in total = 9,000 milliliters

Step-by-step explanation: 25*8=200

225*40=9,000

9,000/1,000=9

9/5 = 1.8

Each teacher bought 1.8 liters = 1,800 milliliters of juice each

The sum of the eigenvalues of matrix A is 8 and the product of eigenvalues is -15.

What is the eigenvalue?

Eigenvalues are the special set of scalar values that are associated with the set of linear equations most probably in the matrix equations. The eigenvectors are also termed characteristic roots.

To find the eigenvalues of matrix A, we can solve the characteristic equation |A - λI| = 0, where λ is a scalar and I is the identity matrix.

|A - λI| = 3- λ 1 4 0 2- λ 6 0 0 5- λ

= (3-λ)(5-λ) - 24 = λ^2 - 8λ - 15

Setting λ^2 - 8λ - 15 = 0, we can find the eigenvalues of the matrix by solving the quadratic equation.

λ^2 - 8λ - 15 = 0

λ = (8 ± √(8^2 + 4*15))/2

λ = (8 ± √(64 + 60))/2

λ = (8 ± √124)/2

So the eigenvalues of matrix A are λ_1 = (8 + √124)/2 and λ_2 = (8 - √124)/2

The sum of eigenvalues is λ_1 + λ_2 = (8 + √124)/2 + (8 - √124)/2 = 8

The product of eigenvalues is λ_1 * λ_2 = (8 + √124)/2 * (8 - √124)/2 = -15

Hence, the sum of the eigenvalues of matrix A is 8 and the product of eigenvalues is -15.

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Answer: 27

Step-by-step explanation:

Given

During 3 days the cat was catching mice

Suppose the first-day joy caught x mice

So, on the second day, it is x+3

on the third day, joy catches twice as many mice as on the first day i.e. 2x

or we can also write, no of mice caught on the second day plus 3 is equal to no of mouse caught on the third day

\(\Rightarrow x+3+3=2x\\\Rightarrow x=6\)

In three day time, it is

\(\Rightarrow x+x+3+2x\\\Rightarrow 4x+3\\\Rightarrow 4\times 6+3=27\)

A variable is a characteristic or attribute that can take on different values. It is an observable and measurable property of an object or phenomenon, which can be used to describe and analyze it.

Parameters are used in inferential statistics to make conclusions about a population based on a sample of data.

(a) If you decide to select based on proportion of 10% from each group, the number of patients selected from each group would be: Group A = (10/100) x 100 = 10 patients Group B = (10/100) x 30 = 3 patients Group C = (10/100) x 30 = 3 patients.

(b) The classified groups can be named as follows: Group A = 10 years of education or less Group B = More than 10 years but less than or equal to 20 years of education Group C = More than 20 years of education.

(c) The sampling method employed in the selection process was stratified sampling. Stratified sampling is a type of probability sampling technique where the population is divided into homogeneous subgroups or strata, and the researcher selects a simple random sample from each subgroup or stratum.

The researcher chooses a proportion of participants from each subgroup to represent the population as a whole, which allows for more precise estimates of the population parameters than simple random sampling.

The sample is selected randomly from the stratified sample, which ensures that the sample is representative of the population.

A variable is a characteristic or attribute that can take on different values. It is an observable and measurable property of an object or phenomenon, which can be used to describe and analyze it.

Variables are used in research to test hypotheses, determine relationships between different phenomena, and make predictions about future outcomes.

A parameter is a numerical summary of a population, which describes a characteristic of the population. It is an unknown constant that can only be estimated from a sample of data.

Parameters are used in inferential statistics to make conclusions about a population based on a sample of data.

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Answer:

It will take 15 hours to read a book with 180 pages

Step-by-step explanation:

First, let's set up a ratio to find how many pages she reads per hour:

36:3 = 12:1

Now we can set up fractions to solve:

\(\frac{12}{1} =\frac{180}{x}\)

Cross multiply:

\(12x=180\)

Divide each side by 12:

\(x=15\)

Answer:

Let Haley be represented as x

Now Mateo has 8 more coins than haley

Mateo = 8 + x

total number of coins is Mateo coins and Haley coins.

x + 8 + x

2x + 8

Given:

Side lengths of rectangle A = 4, 18

One side side length of rectangle B = 36

Required: Possible values for the length of the other side of rectangle B

Explanation:

If the given side length of rectangle B corresponds to the side length, 4 of rectangle A, then the factor is 36/4 = 9.

The length of the other side of rectangle B

If the given side length of rectangle B corresponds to the side length, 18 of rectangle A, then the factor is 36/18 = 2.

The length of the other side of rectangle B

The possible values for the length of the other side of the rectangle B are 162 and 8.

Final Answer: The possible values for the length of the other side of the rectangle B are 162 and 8.

Answer:

Angle VYZ = 27 degrees

A rhombus has 4 equal sides.

That makes Triangle VWX an isosceles triangle.

That means, Angle WXV is also 63 degrees.

All the angles in a triangle add up to 180 degrees:

63 + 63 + x = 180

126 + x = 180

x = 54 degrees

The angle opposite of Angle VWX (Angle VYX) also equals 54 degrees.

That means Angle VYZ = 1/2 of 54 = 27

Angle VYZ = 27 degrees

Answer:

27

Step-by-step explanation:

All triangles have a right angle, and triangles have a total degree of 180.

180 = 90 + 63 + a

a = 27

Answer:

Step-by-step explanation:

The mean for brand A is higher than the mean for brand B

The mean for brand A is higher than the mean for brand B because the mean for A is 1983.33 and the mean for B is 1600 statement (C) is correct.

It is defined as the single number that represents the mean value for the given set of data or the closed value for each entry given in the set of data.

We have:

For brand A:

The number of hours per lightbulb:

1000, 4200, 1400, 1500, 1800, 2000

Mean for brand A:

\(\rm Mean(A) = \frac{Sum \ of \ all \ data \ values}{Number \ of \ data \ in \ the\ set}\)

\(\rm Mean(A)= \frac{1000+4200+1400+1500+1800+ 2000}{6}\)

\(\rm Mean(A)= \frac{11900}{6}\\\\\rm Mean(A) = 1983.33\)

For Brand B:

The number of hours per lightbulb:

1200, 1400, 1600, 1800, 2000

Mean for brand B:

\(\rm Mean(B) = \frac{Sum \ of \ all \ data \ values}{Number \ of \ data \ in \ the\ set}\)

\(\rm Mean(B)= \frac{1200 +1400 +1600 +1800 +2000}{6}\)

\(\rm Mean(B)= \frac{8000}{5}\\\\\rm Mean(B) = 1600\)

We can see that:

Mean(A) > Mean(B)

Thus, the mean for brand A is higher than the mean for brand B because the mean for A is 1983.33 and the mean for B is 1600 statement (C) is correct.

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Answer:

  no

Step-by-step explanation:

If you draw a line from the right end of the top base to the bottom base, parallel to the left side, you cut off a right triangle that has a bottom leg of 12 and two unknown sides (height, and slant length).

All you can say is that the unknown slant length is more than 12 units.

If you know the height, you can find the slant length (hypotenuse) using the Pythagorean theorem.

The linear function that has the same y-intercept as the given graph is the equation y = -2x + 10, corresponding to option 3.

To determine the linear function with the same y-intercept as the graph, we need to find the equation of the line passing through the points (3, 4) and (5, 0).

First, let's find the slope of the line using the formula:

slope (m) = (change in y) / (change in x)

m = (0 - 4) / (5 - 3)

m = -4 / 2

m = -2

Now that we have the slope, we can use the point-slope form of a linear equation to find the equation of the line:

y - y1 = m(x - x1)

Using the point (3, 4) as our reference point, we have:

y - 4 = -2(x - 3)

Expanding the equation:

y - 4 = -2x + 6

Simplifying:

y = -2x + 10

Now, let's check the given options to find the linear function with the same y-intercept:

Option 1: The table with x-values (-3, -1, 1, 3) and y-values (-4, 2, 8, 14)

The y-intercept is not the same as the given line. So, this option is not correct.

Option 2: The table with x-values (-4, -2, 2, 4) and y-values (-26, -18, -2, 6)

The y-intercept is not the same as the given line. So, this option is not correct.

Option 3: The table with x-values (-5, -3, 3, 5) and y-values (-15, -11, 1, 5)

The y-intercept is the same as the given line (10). So, this option is correct.

Option 4: The table with x-values (-6, -4, 4, 6) and y-values (-26, -14, 34, 46)

The y-intercept is not the same as the given line. So, this option is not correct.

Therefore, the linear function that has the same y-intercept as the given graph is the equation y = -2x + 10, corresponding to option 3.

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A company can use 50 plots of lands for buildings.

The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.

Given:

Metropolis requires that for every 5 plots or land used for buildings.

2 plots of land must be left for green space.

A company bought 70 plots of land.

To find the number of green plots:

First, we find the number of green plots.

Applying division operation,

70 ÷ (5 + 2)

= 70 ÷ 7

= 10

Now, the number of green plots,

10 x 2 = 20 green plots.

Subtracting the number of green plots to total number of plots,

70 - 20

= 50 plots.

Therefore, 50 plots can be used for buildings.

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